Find a power series representation for the function f(2) = α 1. f(z) = Σ 3²nn+1 n=0 η 2. f(x) = Σ 3"," n=0 α 3. f(z) = Σ (−1)n3²n₂n+1 n=0 η 4. f(x) = Σ 32n, n=0 6. f(x) Σ 9z+1 = ∞ 5. f(2) = Σ (−1)ngnan n=0 η Σ (-1)ngn,n+1 n=0
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- Find two power series solutions of (x2+2)y"+5xy'-y=0 about the ordinary point x=0. Include the first three terms of each series.For the given periodic function, f(x) =} nx 4 The coefficient a, of the continuous Fourier series associated with the given function f(x) can be computed asIf f(x) = 3 n = 0 - and g(x) = (-1)^x, find the power series of(f(x) + g(x)) and of 1⁄(f(x) − g(x)). n! n = 0 1 / (f(x) + g(x)) = Σ n = 0 ((x)6 – (x)) = n = 0